The wake structure and transition process of a flow past a sphere affected by a streamwise magnetic field

The wake structure and transition process of an incompressible viscous fluid flow past a sphere affected by an imposed streamwise magnetic field are investigated numerically over flow regimes that include steady and unsteady laminar flows at Reynolds numbers up to 300. For cases without a magnetic field, a subregion with the existence of a limit cycle is found in the range $210<Re<270$. The point of division is between $Re=220$ and $Re=230$. For cases with a streamwise magnetic field, five wake patterns are the steady axisymmetric wake with an attached separation bubble, the steady plane symmetric wake with a small spiral dismissed, the steady plane symmetric wake with a limit cycle, the steady plane symmetric wake with a small spiral fed by the upstream fluid and the unsteady plane symmetric wake with a wave-like oscillation or vortex shedding. Under the influence of an imposed streamwise magnetic field, the wake will be transitioned to various patterns. An interesting ‘reversion phenomenon’, which describes the topological structure behind a sphere with a higher Reynolds number and a certain interaction parameter which corresponds to a lower Reynolds number case with a certain interaction parameter or a much lower Reynolds number case without a magnetic field, is also found. The principal results of the present work are summarized in a map of regimes in the $\{N,Re\}$ plane.

New Exact Solutions of Steady Plane Flows of an In Compressible Fluid of Variable Viscosity

<span>Some new exact solutions to the equations governing the steady plane motion of an in compressible<span> fluid of variable viscosity for the chosen form of the vorticity distribution are determined by using<span> transformation technique. In this case the vorticity distribution is proportional to the stream function<span> perturbed by the product of a uniform stream and an exponential stream<br /><br class="Apple-interchange-newline" /></span></span></span></span>

Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow

The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn?0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy.

A class of new exact solutions of the equations governing the steady plane flows of incompressible fluid of variable viscosity

<p>The objective of this paper is to indicate a class of new exact solutions of the equations governing the steady plane flows of incompressible fluid of variable viscosity. The class consists of the stream function characterized by equation (2). Exact solutions are determined for and When is arbitrary we can construct an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution . Therefore, an infinite set of solutions to flow equations. When is not arbitrary, there are two values of and therefore, two exact solutions to flow equations. The streamlines are presented through Fig.(1–56) for some chosen from of f(r).</p>

Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid

In this paper, we derive some exact solutions of the equations governing the steady plane motions of an incompressible second grade fluid. For this purpose, the vorticity and stream functions both are expressed in terms of complex variables and complex functions. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. Some physical features of the derived solutions are also illustrated by their contour plots.

Dynamic Stress Concentration of a Circular Cavity Subjected by Steady Plane SH Waves in an Elastic Quarter with a Semi-Circular Canyon

Steady state responses of a circular cavity and a semi-circular canyon subjected by plane SH wave in an elastic quarter are presented by using Fourier-Hankel wave function expansion method and image method with Fourier series expansion on the boundary conditions to determine linear algebraic equations of unknown wave function coefficients. Especially, displacement and stress component expressions are formulated for incident, reflected, scattering waves, respectively. This method can provide an analytical ideas and methods for further studies of elastodynamic interface problems.